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# In a certain set of five numbers the median is 200

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In a certain set of five numbers the median is 200 [#permalink]  03 Mar 2012, 12:39
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In a certain set of five numbers the median is 200. Is the range greater than 80?

(1) The average (arithmetic mean) of the numbers is 240
(2) Three of the numbers in the set are equal
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Re: In a certain set of five numbers the median is 200 [#permalink]  03 Mar 2012, 14:56
In a certain set of five numbers the median is 200. Is the range greater than 80?

Say the set is {a, b, 200, c, d}. Question: is d-a>80?

(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.

(2) Three of the numbers in the set are equal. Clearly insufficient.

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Re: In a certain set of five numbers the median is 200 [#permalink]  14 May 2013, 19:00
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?

Say the set is {a, b, 200, c, d}. Question: is d-a>80?

(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.

(2) Three of the numbers in the set are equal. Clearly insufficient.

why b is clearly insufficient ?
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Re: In a certain set of five numbers the median is 200 [#permalink]  14 May 2013, 19:32
TheNona wrote:
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?

Say the set is {a, b, 200, c, d}. Question: is d-a>80?

(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.

(2) Three of the numbers in the set are equal. Clearly insufficient.

why b is clearly insufficient ?

Lets say the set is a,b,200,c,d as taken by bunuel...

Now we donot know anything about the mean of the numbers.

If the numbers are 200,200,200,220,230 the range will be 30
If the numbers are 200,200,200,220,290 the range will be 40. and so onnnnnn....

So we cannot say desicively what the range is? Whether it is greater than 80 or not..So it is not sufficient
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Re: In a certain set of five numbers the median is 200 [#permalink]  15 May 2013, 01:33
tom09b wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?

(1) The average (arithmetic mean) of the numbers is 240
(2) Three of the numbers in the set are equal

From F.S 1, as the average is 240, we can assume that each of the 5 elements is 240 . However , as the median is 200, the two elements below the median can be at-most 200 each and the two elements above median can be at-least 200 each. Now,Range = Max(element)-Min(element). After maximizing the 2 elements below the median, we can have the following set : 200,200,200,300,300. Now,to have a value of range=80, we would have to have the value of the Max(element) = 280. Notice : 200,200,200,320,280 --> The Max(element) changes to 320 . Thus, any change on the Max(element) will ALWAYS lead to a range>80.Also, any decrease on the Min(element) will only increase the numerical value of Range above 80. Sufficient.

From F.S 2, we can have either 160,180,200,200,200 where range<80 OR 100,120,200,200,200 where range>80. Insufficient.

A.

Last edited by vinaymimani on 15 May 2013, 13:08, edited 1 time in total.
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Re: In a certain set of five numbers the median is 200 [#permalink]  15 May 2013, 01:46
TheNona wrote:
Bunuel wrote:
In a certain set of five numbers the median is 200. Is the range greater than 80?

Say the set is {a, b, 200, c, d}. Question: is d-a>80?

(1) The average (arithmetic mean) of the numbers is 240 --> the sum of the numbers is 240*5=1,200. Now, let's see whether the range can be less than 80, so let's try to minimize the range. The range will be minimized if we maximize a and minimize d. Maximum value of a as well as b is 200 and minimum value of d is c, so our set will be: {200, 200, 200, d, d} --> 600+2d=1,200 --> d=300 --> the range=d-c=300-200=100>80. Sufficient.

(2) Three of the numbers in the set are equal. Clearly insufficient.

why b is clearly insufficient ?

Because it's easy to construct the sets which give two different answers to the question:
{200, 200, 200, 201, 100000000}
{200, 200, 200, 201, 202}
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Re: In a certain set of five numbers the median is 200   [#permalink] 15 May 2013, 01:46
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